The Chemco Company manufactures car tires that last distances. Assuming such distances are normally distributed with a mean of = 35, 600 miles and a standard deviation of = 4, 280 miles.

(a) If a tire is randomly selected, what is the probability it lasts less than 30, 000 mi.?

(b) If 36 tires are randomly selected, what is the probability they last distances that have a mean less than 30, 000 mi.?

(c) If the manufacturer wants to guarantee the tires so that only 3% will be replaced because of failure before the guaranteed number of miles, for how many miles should the tire be guaranteed?